Needle Decompositions in Riemannian Geometry
Bo'az Klartag, "Needle Decompositions in Riemannian Geometry"
2017 | ISBN-10: 1470425424 | 77 pages | PDF | 1 MB
2017 | ISBN-10: 1470425424 | 77 pages | PDF | 1 MB
The localization technique from convex geometry is generalized to the setting of Riemannian manifolds whose Ricci curvature is bounded from below. In a nutshell, the author's method is based on the following observation: When the Ricci curvature is non-negative, log-concave measures are obtained when conditioning the Riemannian volume measure with respect to a geodesic foliation that is orthogonal to the level sets of a Lipschitz function. The Monge mass transfer problem plays an important role in the author's analysis.